Tax Incidence and Deadweight Loss

Excise Taxes Tax charged on each unit of a good or service that is sold Most common tax Gasoline, cigarettes Local governments impose excise taxes on services (hotel room rentals)

Excise Tax Renting a room in Potterville Without taxes, equilibrium price of a room $80 Equilibrium quantity of hotel rooms rented is 10,000 Now, government imposes an excise tax of $40 per night Means – every time a room is rented for the night, the owner of the hotel must pay the city $40 What does this imply about the supply curve?

The Supply and Demand for Hotel Rooms in Potterville Price of hotel room $140 120 S 100 E Equilibrium price 80 B 60 D 40 Figure Caption: Figure 7-1: The Supply and Demand for Hotel Rooms in Potterville In the absence of taxes, the equilibrium price of hotel rooms is $80 a night, and the equilibrium number of rooms rented is 10,000 per night, as shown by point E. The supply curve, S, shows the quantity supplied at any given price, pre-tax. At a price of $60 a night, hotel owners are willing to supply 5,000 rooms, point B. But post-tax, hotel owners are willing to supply the same quantity only at a price of $100: $60 for themselves plus $40 paid to the city as tax. 20 5,000 10,000 15,000 Quantity of hotel rooms Equilibrium quantity

Excise Tax Graph shows that the post-tax supply curve shifts up by the amount of the tax compared to the pre-tax supply curve At every quantity supplied, the supply price has increased by $40

An Excise Tax Imposed on Hotel Owners Price S $140 Supply curve shifts upward by the amount of the tax 2 120 A S 100 1 E Excise tax = $40 per room 80 60 D B Figure Caption: Figure 7-2: An Excise Tax Imposed on Hotel Owners A $40 per room tax imposed on hotel owners shifts the supply curve from S1to S2, an upward shift of $40. The equilibrium price of hotel rooms rises from $80 to $100 a night, and the equilibrium quantity of rooms rented falls from 10,000 to 5,000. Although hotel owners pay the tax, they actually bear only half the burden: the price they receive net of tax falls only $20, from $80 to $60. Guests who rent rooms bear the other half of the burden, because the price they pay rises by $20, from $80 to $100. 40 20 5,000 10,000 15,000 Quantity of hotel rooms

Excise Tax The graph also shows the results of a quota placed on sales A quota drives a wedge between the price paid by consumers and the price received by producers Excise taxes does the same thing Excise tax on hotel rooms is actually a tax on the producers (hotel owners) not the guest

Excise Tax What happens if the city levied a tax on consumers instead of producers? Hotel guests pay $40 for each night stayed

An Excise Tax Imposed on Hotel Guests Price $140 Demand curve shifts downward by the amount of the tax 120 A S 100 E Excise tax = $40 per room 80 60 D B 1 Figure Caption: Figure 7-3: An Excise Tax Imposed on Hotel Guests A $40 per room tax imposed on hotel guests shifts the demand curve from D1to D2, a downward shift of $40. The equilibrium price of hotel rooms falls from $80 to $60 a night, and the quantity of rooms rented falls from 10,000 to 5,000. Although in this case the tax is officially paid by consumers, while in Figure 7-2 the tax was paid by producers, the outcome is the same: after taxes, hotel owners receive $60 per room but guests pay $100. This illustrates a general principle: The incidence of an excise tax doesn’t depend on whether consumers or producers officially pay the tax. 40 20 D 2 5,000 10,000 15,000 Quantity of hotel rooms

Both graphs show the same price effect Consumers pay an effective price of $100, producers receive an effective price of $60, and 5,000 hotel rooms are bought and sold **It doesn’t matter who officially pays the tax – the equilibrium outcome is the same

Tax Incidence Incidence of a tax is a measure of who really pays it Who really bears the burden of the tax? In reality, between consumers and producers, one group bears more of a burden than the other

Excise Tax Paid by Consumers What determines how the burden of an excise tax is allocated between consumers and producers? Depends on the shape of the supply and demand curve Depends on the price elasticity of supply and the price elasticity of demand

An Excise Tax Paid Mainly By Consumers When the price elasticity of demand is low and the price elasticity of supply is high, the burden of an excise tax falls mainly on consumers. Price of gasoline (per gallon) $2.95 Tax burden falls mainly on consumers Excise tax = $1 per gallon 2.00 S 1.95 Figure Caption: Figure 7-4: An Excise Tax Paid Mainly By Consumers The relatively steep demand curve here reflects a low price elasticity of demand for gasoline. The relatively flat supply curve reflects a high price elasticity of supply. The pre-tax price of a gallon of gasoline is $2.00, and a tax of $1.00 per gallon is imposed. The price paid by consumers rises by $0.95 to $2.95, reflecting the fact that most of the burden of the tax falls on consumers. Only a small portion of the tax is borne by producers: the price they receive falls by only $0.05 to $1.95. D Quantity of gasoline (gallons)

Excise Tax Paid by Consumers Two key assumptions: Price elasticity of demand for gasoline is assumed to be very low, so the demand curve is relatively steep Price elasticity of supply of gasoline is assumed to be very high, so the supply curve is relatively flat **When the price elasticity of demand is low and the price of elasticity of supply is high, the burden of an excise tax falls mainly on consumers **

Excise Tax Paid by Consumers **When the price elasticity of demand is low and the price of elasticity of supply is high, the burden of an excise tax falls mainly on consumers ** WHY? A low price elasticity of demand means that consumers have few substitutes and so little alternatives to buying higher-priced gasoline

An Excise Tax Paid Mainly by Producers Price of parking space When the price elasticity of demand is high and the price elasticity of supply is low, the burden of an excise tax falls mainly on producers. S $6.50 6.00 D Excise tax = $5 per parking space Tax burden falls mainly on producers Figure Caption: Figure 7-5: An Excise Tax Paid Mainly by Producers The relatively flat demand curve here reflects a high price elasticity of demand for downtown parking, and the relatively steep supply curve results from a low price elasticity of supply. The pre-tax price of a daily parking space is $6.00 and a tax of $5.00 is imposed. The price received by producers falls a lot, to $1.50, reflecting the fact that they bear most of the tax burden. The price paid by consumers rises a small amount, $0.50, to $6.50, so they bear very little of the burden. 1.50 Quantity of parking spaces

Excise Tax on Consumers & Producers When the price elasticity of demand is higher than the price elasticity of supply, an excise tax falls mainly on producers. When the price elasticity of supply is higher than the price elasticity of demand, an excise tax falls mainly on consumers Elasticity (not who pays the tax) determines the incidence of an excise tax

Benefits and Costs of Taxation If government is consider whether to impose a tax or how to design a tax system, it must weigh the benefits of a tax against its loses Benefit of a tax is the revenue it raises for the government to pay for these services Although, comes at a cost – cost is normally larger than the amount consumers and producers pay

Revenue from an Excise Tax How much revenue foes the government collect from an excise tax? In example of hotel rooms……amount is equal to the area of the shaded rectangle

The Revenue from an Excise Tax Price of hotel room The tax revenue collected is: Tax revenue = $40 per room × 5,000 rooms = $200,000 $140 120 A S 100 E Excise tax = $40 per room Area = tax revenue 80 60 D B The area of the shaded rectangle is: Area = Height × Width = $40 per room × 5,000 rooms = $200,000 Figure Caption: Figure 7-6: The Revenue from an Excise Tax The revenue from a $40 excise tax on hotel rooms is $200,000, equal to the tax rate, $40—the size of the wedge that the tax drives between the supply price and the demand price—multiplied by the number of rooms rented, 5,000. This is equal to the area of the shaded rectangle. 40 20 6 5,000 10,000 15,000 Quantity of hotel rooms

Revenue from an Excise Tax General Principle: The revenue collected by an excise tax is equal to the area of the rectangle whose height is the tax wedge between the supply and demand curves and whose width is the quantity transacted under the tax.

Tax Rates and Revenue From graph above, $40 per room is the tax rate on hotel rooms Tax rate is the amount of tax levied per unit of whatever is being taxed Tax rates can be in dollar amount per unit of good or service Or they are defined as the percentage of the price

Tax Rates and Revenue Relationship between tax rates and revenue: Not a one-for-one relationship Generally, doubling the excise tax rate on a good or service won’t double the amount of revenue collected, because the tax increase will reduce the quantity of the good or service transacted This relationship is not always positive, some cases raising the tax rate actually reduces the amount of revenue the government collects

Tax Rates and Revenue (a) An excise tax of $20 (b) An excise tax of $60 Price of hotel room Price of hotel room $140 $140 120 120 110 S Area = tax revenue S 90 E E Excise tax = $20 per room Area = tax revenue Excise tax = $60 per room 80 80 70 D D Figure Caption: Figure 7-7: Tax Rates and Revenue In general, doubling the excise tax rate on a good or service won’t double the amount of revenue collected, because the tax increase will reduce the quantity of the good or service bought and sold. And the relationship between the level of the tax and the amount of revenue collected may not even be positive. Panel (a) shows the revenue raised by a tax rate of $20 per room, only half the tax rate in Figure 7-6. The tax revenue raised, equal to the area of the shaded rectangle, is $150,000, three- quarters as much as the revenue raised by a $40 tax rate. Panel (b) shows that the revenue raised by a $60 tax rate is also $150,000. So raising the tax rate from $40 to $60 actually reduces tax revenue. 50 40 40 20 20 6 ,000 7,500 10,000 15,000 2,500 5,000 10,000 15,000 Quantity of hotel rooms Quantity of hotel rooms

Tax Rates and Revenue Setting a tax rate high deters a significant number of transactions which is likely to lead to a fall in tax revenue Two ways to think about this: 1. tax increase means that the government raises more revenue for each unit of the good sold, which other think equal would lead to a rise in tax revenue

Tax Rates and Revenue The tax increase reduces the quantity of sales, which other thinks equal would lead to a fall in tax revenue What is the end result? Depends both on the price elasticizes of supply and demand and on the initial level of tax

Tax Rates and Revenue If the price elasticities of both supply and demand are low, the tax increase won’t reduce the quantity of the good sold very much, so that the tax revenue would definitely rise If the price elasticities are high, the result is less certain; of they are high enough, the tax reduces the quantitative sold so much that the tax revenue falls Also, if the initial tax rate is low, the government doesn't lose much revenue from the decline in the quantity of the good sold, so the tax increase will definitely increase tax revenue

Tax Rates and Revenue Also, if the initial tax rate is low, the government doesn't lose much revenue from the decline in the quantity of the good sold, so the tax increase will definitely increase tax revenue If the initial tax rate is high, the result again is less certain Tax revenue is likely to fall or rise very little from a tax increase only in cases where the price elasticities are high and there is already a high tax rate

The Costs of Taxation What is the cost of taxation? Actually, a tax, like a quota, prevents mutually beneficial transactions from occurring Remember the tax on hotel rooms? Due to the wedge created by the tax, some transactions don’t occur that would have occurred without the tax Remember deadweight loss? The cost to society is inefficient—the value of the forgone mutually beneficial transactions

A Tax Reduces Consumer and Producer Surplus i c e Fall in consumer surplus due to tax S P C A B Excise tax = T P E E F C Fall in producer surplus due to tax P P Figure Caption: Figure 7-8: A Tax Reduces Consumer and Producer Surplus Before the tax, the equilibrium price and quantity are PE and QE, respectively. After an excise tax of T per unit is imposed, the price to consumers rises to PC and consumer surplus falls by the sum of the dark blue rectangle, labeled A, and the light blue triangle, labeled B. The tax also causes the price to producers to fall to PP; producer surplus falls by the sum of the dark red rectangle, labeled C, and the light red triangle, labeled F. The government receives revenue from the tax, QT× T, which is given by the sum of the areas A and C. Areas Band F represent the losses to consumer and producer surplus that are not collected by the government as revenue; they are the deadweight loss to society of the tax. D Q Q T E Quantity

 A tax reduces both, the CS and the PS Tax Rates and Revenue A fall in the price of a good generates a gain in consumer surplus. Similarly, a price increase causes a loss to consumers. So it’s not surprising that in the case of an excise tax, the rise in the price paid by consumers causes a loss. Meanwhile, the fall in the price received by producers leads to a fall in producer surplus.  A tax reduces both, the CS and the PS

Tax Rates and Revenue Using a triangle to measure deadweight loss is a technique used in many economic applications Used to measure deadweight loss produces by types of taxes other than excise tax, used to measure deadweight loss produced by monopolies, used to evaluate the benefits and costs of public policies because taxation

Tax Rates and Revenue When looking at the total amount of inefficiency caused by a tax, we must also take into account resources actually used by the government to collect the tax, and by taxpayers to pay it, over and above the amount of the tax Administrative costs of taxes are the resources lost i.e. the amount of time people spend filling out their income tax forms and or the money they spend paying someone else to prepare their tax forms

Tax Rates and Revenue The total inefficiency caused by a tax is the sum of its deadweight loss and its administrative costs. The general rule for economic policy is that, other things equal, a tax system should be designed to minimize the total inefficiency it imposes on society.

Elasticities and the Deadweight Loss of a Tax We know (hopefully) that the deadweight loss from an excise tax arises because it prevents some mutually beneficial transactions from occurring The producer and consumer surplus that is forgone because of these missing transactions is equal to the size of the deadweight loss itself Larger the number of transactions that are prevented by the tax, the larger the deadweight loss

Elasticities and the Deadweight Loss of a Tax To minimize the efficiency costs of taxation, one should choose to tax only those goods for which demand or supply, or both, is relatively inelastic. For such goods, a tax has little effect on behavior because behavior is relatively unresponsive to changes in the price.

Elasticities and the Deadweight Loss of a Tax In the extreme case in which demand is perfectly inelastic (a vertical demand curve), the quantity demanded is unchanged by the imposition of the tax. As a result, the tax imposes no deadweight loss. Similarly, if supply is perfectly inelastic (a vertical supply curve), the quantity supplied is unchanged by the tax and there is also no deadweight loss If the goal in choosing whom to tax is to minimize deadweight loss, then taxes should be imposed on goods and services that have the most inelastic response—that is, goods and services for which consumers or producers will change their behavior the least in response to the tax.

Deadweight Loss and Elasticities (a) Elastic Demand (b) Inelastic Demand Price Price S S Deadweight loss is larger when demand is elastic P C Excise tax = T P C E Deadweight loss is smaller when demand is inelastic P P E E E Excise tax = T P P D Figure Caption: Figure 7-10: Deadweight Loss and Elasticities Demand is elastic in panel (a) and inelastic in panel (b), but the supply curves are the same. Supply is elastic in panel (c) and inelastic in panel (d), but the demand curves are the same. The deadweight losses are larger in panels (a) and (c) than in panels (b) and (d) because the greater the price elasticity of demand or supply, the greater the tax-induced fall in the quantity transacted. In contrast, the lower the price elasticity of demand or supply, the smaller the tax-induced fall in the quantity transacted and the smaller the deadweight loss. P P D Q Q Quantity Q Q Quantity T E T E

Deadweight Loss and Elasticities (c) Elastic Supply (d) Inelastic Supply Price Price S Deadweight loss is larger when supply is elastic P C S P Excise tax = T C P P E Deadweight loss is smaller when supply is inelastic E E Excise tax = T E P P Figure Caption: Figure 7-10: Deadweight Loss and Elasticities Demand is elastic in panel (a) and inelastic in panel (b), but the supply curves are the same. Supply is elastic in panel (c) and inelastic in panel (d), but the demand curves are the same. The deadweight losses are larger in panels (a) and (c) than in panels (b) and (d) because the greater the price elasticity of demand or supply, the greater the tax-induced fall in the quantity transacted. In contrast, the lower the price elasticity of demand or supply, the smaller the tax-induced fall in the quantity transacted and the smaller the deadweight loss. P P D D Q Q Quantity Q Q Quantity T E T E

Elasticities and the Deadweight Loss of a Tax From the graphs, it is easily seen that to minimize the efficiency costs of taxation, you should choose to tax only those goods for which demand or supply, or both, is relatively inelastic For these goods, tax has little effect on the behavior because behavior is relatively unresponsive to changes in the price